@Tim I didn't call it a mistake. A Yale educated chief executive does not simply pronounce this word incorrectly as a mistake. It is a term with a legit origin.
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cwallenpooleJun 7 '11 at 3:25

1

Physicist Richard Muller addressed the pronunciation of nuclear at some length in the UC Berkeley "Physics 10" (AKA "Physics for Future Presidents") course. For one, "nucular" is how the nuclear power industry pronounces it, but I don't recall the rest. It should be possible to find the exact lecture.
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Peter MortensenJun 7 '11 at 6:37

Some people call it Nucular just cause Homer Simpson do it :P
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MiPnamicJun 7 '11 at 6:51

2 Answers
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Steven Pinker has proposed a phonotactic explanation for the conversion of nuclear to nucular: the unusual and disfavored sequence [kli.ər] is gradually transformed to a more acceptable configuration via metathesis.

However, Arnold Zwicky notes that [kli.ər] presents no difficulty for English speakers in words such as pricklier. He also regards the proposition of metathesis as unnecessary. Zwicky suggests a morphological origin, combining the slang nuke with the common sequence -cular (molecular, particular, etc.). Supporting Zwicky's hypothesis, Geoffrey Nunberg quotes a government weapons specialist: "Oh, I only say 'nucular' when I'm talking about nukes." Nunberg argues that this pronunciation by weapons specialists and by politicians such as Bush – who are aware of the more accepted pronunciation – may be a "deliberate choice". He suggests that the reasons for this choice are to "assert authority" or to sound folksy.

I personally find the Zwicky hypothesis more compelling: the pronunciation is formed by analogy with words like "molecular" and "particular". But both are possible, and in fact, it doesn't necessarily have to be the same method of production for all speakers — there could be interspeaker variation.

(Note that Zwicky's explanation isn't actually "metathesis" per se at all; instead, being nuke + ular, it is formed "as it should be".)

Always thought it was on account of the Merkins...(joke)
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Rory AlsopJun 6 '11 at 22:53

It could be a bit of both. Nuke + -ular is a valid analysis, but pricklier might not be a valid counterexample because the /l/ is phonemically (if not always phonetically) syllabic, and the /ɪ/ in pricklier creates a rather different environment for sound changes than the /u/ in nuclear.
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Jon PurdyJun 6 '11 at 23:20

It occurred to me that very few other words have the syllabic make-up of nùclear,
but there is a host of words in `-cular (with antepenultimate stress) eg binocular, vascular, muscular, particular, spectacular to name a few.

Thus the shift nuclear > nucular makes perfectly good sense, as a case where an isolated make-up is adapted to a more prevalent pattern.